We investigate grokking in transformers through the lens of inductive bias: dispositions arising from architecture or optimization that let the network prefer one solution over another. We first show that architectural choices such as the position of Layer Normalization (LN) strongly modulates grokking speed. This modulation is explained by isolating how LN on specific pathways shapes shortcut-learning and attention entropy. Subsequently, we study how different optimization settings modulate grokking, inducing distinct interpretations of previously proposed controls such as readout scale. Particularly, we find that using readout scale as a control for lazy training can be confounded by learning rate and weight decay in our setting. Accordingly, we show that features evolve continuously throughout training, suggesting grokking in transformers can be more nuanced than a lazy-to-rich transition of the learning regime. Finally, we show how generalization predictably emerges with feature compressibility in grokking, across different modulators of inductive bias. Our code is released at https://tinyurl.com/y52u3cad.
College of Engineering, Computing and Cybernetics（工程、计算与控制学院）；The Australian National University（澳大利亚国立大学）；School of Physics and Astronomy（物理与天文学院）；Tel-Aviv University（特拉维夫大学）
Neural networks sometimes exhibit grokking, a phenomenon where perfect or near-perfect performance is achieved on a validation set well after the same performance has been obtained on the corresponding training set. In this workshop paper, we introduce a robust technique for measuring grokking, based on fitting an appropriate functional form. We then use this to investigate the sharpness of transitions in training and validation accuracy under two settings. The first setting is the theoretical framework developed by Levi et al. (2023) where closed form expressions are readily accessible. The s…
Flatness is Necessary, Neural Collapse is Not: Rethinking Generalization via Grokking
Ting Han Lamarr Institute, TU Dortmund, Germany（廷汉拉马尔研究所，杜伊斯堡-艾森大学，德国）；Institute for AI in Medicine, UK Essen（人工智能医学研究所，英国埃森）；Research Center Trustworthy Data Science and Security of the University Alliance Ruhr, TU Dortmund, Germany（trustworthy数据科学与安全研究所以及鲁尔大学联盟，杜伊斯堡-艾森大学，德国）；Ruhr University Bochum, Germany（波恩鲁尔大学，德国）；Department of Physics, TU Dortmund, Germany（物理系，杜伊斯堡-艾森大学，德国）；Lamarr Institute, TU Dortmund, Germany（廷汉拉马尔研究所，杜伊斯堡-艾森大学，德国）
The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the underpinnings of Grokking via a series of empirical studies. Specifically, we uncover an optimization anomaly plaguing adaptive optimizers at extremely late stages of training, referred to as the Slingshot Mechanism. A prominent artifact of the Slingshot Mechanism can be measured by the cyclic phase transitions between stable and unstable training regimes, an…
Two Speeds of Learning: A Representation-Readout Decomposition of Grokking and Double Descent
Center for Computational Neuroscience（计算神经科学中心）；Flatiron Institute（Flatiron研究所）；Department of Physics（物理系）；Harvard University（哈佛大学）；Kempner Institute（Kempner研究所）；New York University（纽约大学）
By their nature, the composition of black box models is opaque. This makes the ability to generate explanations for the response to stimuli challenging. The importance of explaining black box models has become increasingly important given the prevalence of AI and ML systems and the need to build legal and regulatory frameworks around them. Such explanations can also increase trust in these uncertain systems. In our paper we present RICE, a method for generating explanations of the behaviour of black box models by (1) probing a model to extract model output examples using sensitivity analysis; …
Explaining Neural Networks in Preference Learning: a Post-hoc Inductive Logic Programming Approach
Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy（意大利拉奎拉大学信息工程、计算机科学与数学系）；Department of Life, Health and Environmental Sciences, University of L'Aquila, Italy（意大利拉奎拉大学生命、健康与环境科学系）；Department of Electrical Engineering and Information Technologies, University of Naples, Italy（意大利那不勒斯大学电气工程与信息技术系）；Ethos Group, Department of Human Sciences, University of Verona, Italy（意大利维罗纳大学人文科学系Ethos研究组）
Learning from demonstration is an effective method for human users to instruct desired robot behaviour. However, for most non-trivial tasks of practical interest, efficient learning from demonstration depends crucially on inductive bias in the chosen structure for rewards/costs and policies. We address the case where this inductive bias comes from an exchange with a human user. We propose a method in which a learning agent utilizes the information bottleneck layer of a high-parameter variational neural model, with auxiliary loss terms, in order to ground abstract concepts such as spatial relat…
Theoretical Investigation on Inductive Bias of Isolation Forest
National Key Laboratory for Novel Software Technology, Nanjing University, China（新型软件技术国家实验室，南京大学）；School of Artificial Intelligence, Nanjing University, China（人工智能学院，南京大学）；School of Intelligence Science and Technology, Nanjing University, China（智能科学与技术学院，南京大学）；College of Computer and Information, Hohai University, China（计算机与信息学院，河海大学）；Key Laboratory of Water Resources Big Data Technology of Ministry of Water Resources, Hohai University, China（水利部水资源大数据技术重点实验室，河海大学）
